Etymology
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arbitrary (adj.)

c. 1400, "deciding by one's own discretion, depending on one's judgment," from Latin arbitrarius "of arbitration," hence "depending on the will, uncertain," from arbiter (see arbiter). The meaning in English gradually descended to "capricious, ungoverned by reason or rule, despotic" (1640s). Related: Arbitrarily; arbitrariness.

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Definitions of arbitrary

arbitrary (adj.)
based on or subject to individual discretion or preference or sometimes impulse or caprice;
the arbitrary rule of a dictator
arbitrary division of the group into halves
an arbitrary choice
an arbitrary decision
of arbitrary size and shape
an arbitrary penalty
From wordnet.princeton.edu